Explanation

The sum of odd integers from 1 to 100 are - 1 + 3 + 5 + 7 + ……… + 99.

This is an Arithmetic Progression with the following parameters: First Number, a = 1 Last Number, l = 99 Common Difference, d = 2 So, the Number of terms in the Arithmetic Progression, n = (l - a)/d + 1 = (99 - 1)/2 + 1 = 98/2 + 1 = 49 + 1 = 50 So, the sum of the Arithmetic Progression, S = n/2(l + a) = 50/2(99 + 1) = 25 X 100 = 2500 So, the sum of odd integers from 1 to 100 = 2500